Course goals and learning outcomes support the Foundational Component Areas defined by the Texas Higher Education Coordinating Board. Course goals are linked to the respective Core Curriculum Competencies: Critical Thinking Skills, Communication Skills, and Empirical and Quantitative Skills. Specific competencies are identified in designated course goals and learning outcomes.

Upon successful completion of this course, students will:

Apply calculus to solve business, economics, and social sciences problems by
1. defining the derivative as a rate of change;
2. calculating marginal cost and marginal revenue;
3. calculating average cost.
Apply appropriate differentiation techniques to obtain derivatives of various functions, including logarithmic and exponential functions by
1. using the definition of the derivative to find derivatives of functions;
2. using the derivative to find the slope of a tangent to a curve;
3. finding derivatives of functions using the product, quotient, power, and chain rules;
4. finding derivatives of algebraic, exponential, and logarithmic functions;
5. finding higher order derivatives.
Solve application problems involving implicit differentiation and related rates by
1. finding the derivative of a function using implicit differentiation;
2. using implicit differentiation to calculate such quantities as marginal propensity to consume and save.
Solve optimization problems with emphasis on business and social sciences applications by
1. using the first derivative test to find relative maxima and minima of a function;
2. finding the extreme values of a function on a closed interval;
3. checking a function for concavity and inflection points;
4. using the first derivative test to identify the intervals on which a function is increasing or decreasing;
5. applying the second derivative test to identify relative extrema;
6. producing a graph of a function using information obtained from the first and second derivatives of that function;
7. solving applied optimization problems, including the calculation of minimum cost, maximum revenue, and maximum profit.
Determine appropriate technique(s) of integration by
1. defining antiderivatives and indefinite integrals;
2. applying techniques of integration;
3. applying the Fundamental Theorem of Calculus;
4. evaluating definite integrals;
5. finding a particular antiderivative satisfying initial conditions.
Integrate functions using the method of integration by parts or substitution, as appropriate, by
1. developing the u-substitution method of integration;
2. applying the u-substitution method of integration.
Solve business, economics, and social sciences applications problems using integration techniques by
1. finding the area between two curves;
2. calculating producer and consumer surplus;
3. finding the average value of a function.
Apply the concept of a limit to real-valued functions by
1. evaluating limits;
2. applying the basic properties of limits;
3. evaluating one-sided limits;
4. evaluating infinite limits;
5. evaluating limits at infinity.
Demonstrate an understanding of continuous and discontinuous functions by
1. finding points of discontinuity of a function;
2. determining whether a function is discontinuous at a point using the definition of continuity;
3. determining the horizontal and vertical asymptotes of a function.
Critical Thinking Skills: Demonstrate the ability to evaluate, synthesize, and perform inquiry and analysis of information in mathematical problems by
1. predicting and verifying when to use integration by parts and/or substitution;
2. determining whether a function is discontinuous or continuous.
Communication Skills: Demonstrate the ability to communicate orally, visually, and/or in writing using mathematical language and symbols by
1. solving and graphing optimization problems;
2. illustrating the solution steps to find derivatives of functions.
Empirical and Quantitative Skills: Manipulate and analyze numerical data or observable facts in making informed conclusions by
1. evaluating limits;
2. using calculus to calculate surplus and marginal values.

MATH 1325

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MATH 1325 - Calculus for Business and Social Sciences